Superconducting Niobium Air Bridges

• Superconducting niobium air bridges are microscale structures that interconnect superconducting layers in quantum and microwave circuits, ensuring low loss and robust performance.
• They are fabricated using advanced techniques such as aluminum hard masks and two-photon lithography to achieve high yield and precise geometries vital for minimizing parasitic modes.
• Their optimized superconducting and microwave properties boost coherence in quantum hardware by suppressing unwanted interference and ensuring reliable high-field operation.

Superconducting niobium air bridges are mesoscale or microscale structures of niobium metal fabricated to electrically connect separated superconducting planes or lines in planar circuits, physically crossing regions without direct substrate contact and thus forming a "bridge" suspended above the surface. These components are critical in the architecture of advanced superconducting microwave and quantum circuits, serving functions from suppression of parasitic modes and cross-talk to enabling compact, multilayer circuit topologies. The essential requirements for these structures are exceptionally low microwave loss, mechanical robustness, superconducting integrity under varying thermal and magnetic environments, and manufacturability with high yield and scalability.

1. Superconducting Properties and Functional Advantages

Niobium is favored for air bridges due to its high superconducting transition temperature ($T_c \sim 9.2$ K), its large energy gap ($\Delta(0) = 2.1$ meV for sputtered films), and its type-II superconductivity below $T_c$, with upper critical fields exceeding 2 T for thin films and bridges. The superconducting properties, especially the large energy gap and high $T_c$, translate directly to operational advantages: niobium air bridges remain lossless at temperatures and magnetic fields where aluminum-based alternatives fail, and exhibit lower microwave loss due to reduced quasiparticle excitation at the operating point (Thiemann et al., 2014, Bruckmoser et al., 15 Mar 2025, Arlt et al., 13 Aug 2025).

Key microwave parameters are determined by the complex conductivity $\sigma=\sigma_1-i\sigma_2$. The imaginary part, linked to kinetic inductance and lossless supercurrent response, for niobium is given by

$$\frac{\sigma_2(T)}{\sigma_n} \approx \frac{\pi \Delta(T)}{\hbar \omega} \tanh \left[\frac{\Delta(T)}{2k_B T}\right]$$

where $\Delta(T)$ is fitted by

$$\Delta(T) \approx \Delta(0)\sqrt{3.016(1-T/T_c)-2.4(1-T/T_c)^2}$$

Substantial deviation from weak-coupling BCS ($2\Delta(0)\approx5.3k_BT_c$) implies strong electron-phonon coupling in Nb, resulting in robust gap suppression only at much higher thermal energies (Thiemann et al., 2014).

Surface resistance $R_s$ of high-quality niobium films and bridges at low temperatures follows $R_s\propto\nu^2$, with values matching or slightly exceeding Pb due to process-induced non-superconducting defects, reinforcing the need for process optimization (Thiemann et al., 2014, Bruckmoser et al., 15 Mar 2025).

Superconducting bridges fabricated with dimensions comparable to the coherence length can act as Josephson contacts, supporting phase-coherent transport over the bridge and participating in quantum interference in devices such as SQUIDs (Bondarenko et al., 2022, Uhl et al., 2023).

2. Fabrication Processes and Engineering Considerations

Fabricating niobium air bridges presents unique challenges due to film stress, substrate interactions, and the need for low-loss interfaces. Established processes include the subtractive method using an aluminum hard mask and lift-off for high-yield, high-integrity bridges (Bruckmoser et al., 15 Mar 2025), the two-photon lithography (TPL) process for advanced 3D resist scafolding (Huang et al., 13 Mar 2025), gradient exposure for precise photoresist arch definition (Sun et al., 17 Jun 2025), and the integration in industry-scale processes using dielectric encapsulation and photoresist reflow (Arlt et al., 13 Aug 2025).

A concise overview is shown below:

Process	Key Step (Masking/Patterning)	Maximum Demonstrated Bridge Length	Remarks
Aluminum hard mask	Tilted Al deposition, lift-off	Not specified	Low-loss, robust bridges (Bruckmoser et al., 15 Mar 2025)
Two-photon lithog.	3D resist scaffold, metal evaporation	$100\,\mu$m	3D profiles, high mechanical strength (Huang et al., 13 Mar 2025)
Gradient exposure	Calibrated photoresist exposure	$30\,\mu$m tested	Precise arch, single-layer resist (Sun et al., 17 Jun 2025)
Industry-scale	SiN encapsulation, resist reflow	Not specified	Scalable to 200 mm wafer (Arlt et al., 13 Aug 2025)

Use of a sacrificial hard mask (e.g., 100 nm Al) provides three functionalities: protection of the resist during argon ion milling, shielding during Nb sputtering (to prevent resist-metal mixing), and acting as an etch stop during SF$_6$ RIE defined bridge patterning. Clean removal ensures minimal residue and high $Q$ (Bruckmoser et al., 15 Mar 2025).

The TPL process allows complex 3D air bridges, but deposition conditions (thermal evaporation vs. sputtering) must match niobium’s mechanical and kinetic properties. For high-throughput and large-scale compatibility, reflowed photoresist arches and encapsulation/dielectric etching are used in semiconductor fabs; process tuning is required to avoid increased TLS dielectric loss due to trapped remnants (e.g., photoresist or SiN) (Arlt et al., 13 Aug 2025).

Gradient exposure eliminates the need for high-temperature reflow, reducing risk of interfacial amorphous layers that could increase decoherence, particularly for Josephson-based circuits (Sun et al., 17 Jun 2025). Calibration with a generalized Beer's law enables precise thickness control for arch geometry:

$$z = z_0 + \frac{1}{\alpha} \ln \left( \frac{P_{z_0-z}}{P - P_0} \right)$$

3. Microwave Loss, Critical Parameters, and Reliability

Internal loss from niobium air bridges is characterized by measurements in the single-photon regime and at higher photon occupancy, decomposed as

$$\delta(n) = \frac{F \delta_{\text{TLS}}^0}{\sqrt{1 + (n/n_c)^\beta}} + \delta_0$$

where $F \delta_{\text{TLS}}^0$ captures dielectric losses from two-level systems (TLS), $n_c$ is the critical photon occupation (TLS saturation threshold), and $\delta_0$ is non-TLS power-independent loss (Arlt et al., 13 Aug 2025).

Rigorous cleaning and process tuning (e.g., optimized Al mask removal, controlled BOE SiN etch) reduce $\delta_0$ to below the detection threshold, with measured mean internal quality factors $Q_{\mathrm{int}}$ exceeding $8.2\times10^6$ (bridging) and $6.0\times10^6$ (in-line) in the single-photon regime; the additional loss per bridge is $\delta_{\mathrm{int}} < 5 \times 10^{-10}$ (Bruckmoser et al., 15 Mar 2025). At higher photon populations, the suppression of slotline and parasitic modes results in an increase in $Q_{\mathrm{int}}$ relative to unbridged devices (Arlt et al., 13 Aug 2025).

Superconducting transition temperatures of bridges ($T_{c,AB}\approx9.32$ K) are close to base films ($T_{c,film}\approx9.43$ K). The critical magnetic fields, fit using

$B_{c2}(T) = B_{c2,0}(1 - T/T_c)$

reveal robust resilience with $B_{c2,0}$ of 2.84 T (in-plane), matching requirements for quantum applications under strong fields (Bruckmoser et al., 15 Mar 2025).

Careful control of niobium purity and surface oxidation is necessary: ultra-high purity minimizes flux trapping and maximizes critical current; surface oxidation reduces magnetization hysteresis, lowering resistive dissipation (Alekseevskiy et al., 2 Jun 2025). The critical current $I_c$ can exceed traditional Silsbee-limited values ($I_c = 5r H_c$) if the current distribution is engineered for "force-free" (i.e., $i\times b=0$) operation, significant for bridge design in high-field environments.

4. Applications in Quantum Hardware and Circuit Integration

Niobium air bridges are essential for routing ground plane connections over transmission lines in coplanar waveguide (CPW) and lumped element circuits, suppressing slotline and other parasitic modes that manifest as low-energy chip resonances deleterious to coherence in quantum hardware (Huang et al., 13 Mar 2025, Bruckmoser et al., 15 Mar 2025, Arlt et al., 13 Aug 2025). The realization of multimode routing in CPW geometries and multi-layer quantum architectures is directly enabled by reliable air bridge technology.

Their integration into transmon qubits—either as vacuum-gap capacitors (where approximately 42% of electric energy is stored in vacuum, reducing surface dielectric loss) or as direct connectivity—has been experimentally validated, yielding median qubit lifetimes $T_1 \approx 51.6\,\mu$s and echo times $T_{2,E}$ up to $88\,\mu$s (Bruckmoser et al., 15 Mar 2025). Lifetimes are presently limited by increased metal-air participance but remain competitive for scalable hardware. In hybrid quantum systems, niobium air bridges and nanobridge Josephson junctions facilitate strong flux tunability and are robust under magnetic and thermal variations, essential for control in hybrid magnonic or optomechanical systems (Uhl et al., 2023).

Application is not limited to resonators; bridge-based Josephson junctions formed via 3D nanobridge fabrication, including gate-tunable designs, support flexible control of critical current and, by extension, circuit properties (Yu et al., 2023, Joint et al., 12 May 2024). The internal control over $I_c(V_g)$,

$$I_c(V_g) \approx I_{c0} \left(1 - \frac{V_g}{V_g^c}\right),$$

enables high integration density circuit design without bulky on-chip magnetic coils.

5. Scaling, Manufacturing, and Process Robustness

Adoption of niobium air bridges in foundry-compatible, high-volume processes has been demonstrated on 200 mm wafers, with integration steps such as encapsulation (PECVD SiN), photoresist reflow for tape-arch definition, and selective dielectric removal with BOE etch (Arlt et al., 13 Aug 2025). High $Q_{\mathrm{int}}$ values ($>10^6$) in the single-photon regime are maintained, bridging the gap between laboratory demonstrations and industrial quantum circuit fabrication.

Yield is improved with low-temperature processes such as gradient exposure (which forgoes high-T resist reflow) and careful dosage calibrations, enabling thousands of bridges to be produced across a wafer with excellent uniformity and mechanical reliability (Sun et al., 17 Jun 2025).

A potential challenge is the introduction of additional TLS loss due to residual dielectric (SiN, resist) from process steps—an effect most prominent at low microwave powers (Huang et al., 13 Mar 2025, Arlt et al., 13 Aug 2025). A plausible implication is that further advances in cleaning, encapsulant engineering, and mask strategy may be required to reach the ultimate loss floor dictated by the intrinsic niobium properties and interface quanta.

6. Outlook and Fundamental Design Implications

Optimizing niobium air bridge performance requires control over purity, geometry, and interface quality, guided by the following principles:

1. Superconducting Integrity: $T_c$, $B_{c2}$, and energy gap determine operating envelope; bridges should match or exceed substrate film $T_c$ and maintain sufficient critical current under anticipated current loading.
2. Microwave Performance: Losses are minimized by engineering for maximal kinetic inductance $L_k$ and low surface resistance $R_s$, directly tied to process quality.
3. Magnetic and Mechanical Robustness: High $B_{c2}$ and force-free current engineering allow operation in high-field environments, while attention to arch geometry yields sturdy, damage-resistant interconnects.
4. Compatibility and Yield: Processes such as subtractive patterning with metal hard masks, gradient exposure, and encapsulation/reflow scaling ensure compatibility with multilayer and multi-chip integration, essential for quantum processor scale-up.
5. Quantum Device Impact: Bridges are not only interconnects but also serve as low-loss capacitive elements and can be engineered as Josephson junctions, supporting rich quantum circuit functionality including tunable qubits, SQUIDs, and switching elements for logic and readout.

Research continues toward process improvements for further reducing stray TLS loss, mechanical decoherence, and variability, along with innovations in three-dimensional nanofabrication, supported by comprehensive characterization of superconducting properties across the phase space spanned by purity, geometry, and electromagnetic environment.

• (Thiemann et al., 2014) Niobium stripline resonators for microwave studies on superconductors
• (Bondarenko et al., 2022) Electrical breakdown of a dielectric for the formation of a superconducting nanocontact
• (Uhl et al., 2023) Niobium Quantum Interference Microwave Circuits with Monolithic Three-Dimensional (3D) Nanobridge Junctions
• (Yu et al., 2023) Gate-Tunable Critical Current of the Three-Dimensional Niobium Nano-Bridge Josephson Junction
• (Joint et al., 12 May 2024) Dynamics of Gate-Controlled Superconducting Dayem Bridges
• (Huang et al., 13 Mar 2025) Fabrication of Metal Air Bridges for Superconducting Circuits using Two-photon Lithography
• (Bruckmoser et al., 15 Mar 2025) Niobium Air Bridges as a Low-Loss Component for Superconducting Quantum Hardware
• (Alekseevskiy et al., 2 Jun 2025) Superconducting properties of ultrapure niobium
• (Sun et al., 17 Jun 2025) Fabrication of airbridges with gradient exposure
• (Arlt et al., 13 Aug 2025) High-$Q$ superconducting resonators fabricated in an industry-scale semiconductor-fabrication facility